The replacement cost is calculated at the netting set level as a simple algebraic sum (floored at zero) of the derivatives’ market values at the reference date. Thus, using the market values indicated in the table (expressed in thousands):

RC = max {V - C; 0} = max {30 - 20 + 50; 0} = 60
 

Since V-C is positive (equal to V of 60,000), the value of the multiplier is 1, as explained in the Standards.

All the transactions in the netting set belong to the interest rate asset class. So the Add-on for interest rate class must be calculated as well as the multiplier since

PFE = multiplier × Add-on_agg
 

For the calculation of the interest rate add-on, the three trades must be assigned to a hedging set (based on the currency) and to a maturity category (based on the end date of the transaction). In this example, the netting set is comprised of two hedging sets, since the trades refer to interest rates denominated in two different currencies (USD and EUR). Within hedging set “USD”, Trade 1 falls into the third maturity category (>5 years) and Trade 2 falls into the second maturity category (1-5 years). Trade 3 falls into the third maturity category (>5 years) of hedging set “EUR”.

S and E represent the start date and end date, respectively, of the time period referenced by the interest rate transactions.

The following table illustrates the steps typically followed for the add-on calculation:

   Calculate Effective Notional Amount

The adjusted notional of each trade is calculated by multiplying the notional amount by the calculated supervisory duration SD as defined in the Standards.

d = Trade Notional × SD = Trade Notional × (exp(-0.05×S) – exp(-0.05 × E)) / 0.05

   Calculate Maturity Category Effective Notional

A supervisory delta is assigned to each trade in accordance with the Standards. In particular:

1. •Trade 1 is long in the primary risk factor (the reference floating rate) and is not an option so the supervisory delta is equal to 1.
2. •Trade 2 is short in the primary risk factor and is not an option; thus, the supervisory delta is equal to -1.
3. •Trade 3 is an option to enter into an interest rate swap that is short in the primary risk factor and therefore is treated as a purchased put option. As such, the supervisory delta is determined by applying the relevant formula using 50% as the supervisory option volatility and 1 (year) as the option exercise date. Assume that the underlying price (the appropriate forward swap rate) is 6% and the strike price (the swaption’s fixed rate) is 5%.

The trade-level supervisory delta is therefore:

Trade	Delta	nstrument Type
Trade 1	1	inear, long (forward and swap)
Trade 2	-1	inear, short (forward and swap)
Trade 3	$$$$	purchased put option

The Maturity Factor MF is 1 for all the trades since they are un-margined and have remaining maturities in excess of one year.

Based on the maturity categories, the Effective Notional D for the USE and EUR hedging sets at the level of the maturity categories are as shown in the table below:

In particular:

Hedging set USD, time bucket 3: D = 1 * 78,693,868 * 1 = 78,693,868

Hedging set USD, time bucket 2: D = -1 * 36,253,849 * 1 = -36,253,849

Hedging set EUR, time bucket 3: D = -0.27 * 37,427,961 * 1 = -10,105,550

   Apply Supervisory Factor

The add-on must be calculated for each hedging set.

For the USD hedging set there is partial offset between the two USD trades:

Effective notional^(IR) _{USD =} [D2² + D3² + 1.4 x D2 x D3]^1/2

   = [(-36,253,849)² + 78,693,868² + 1.4 × (-36,253,849) × 78,693,868]^1/2

   = 59,269,963

For the Hedging set EUR there is only one trade (and one maturity category):

  Effective notional^(IR)_EUR = 10,105,550

In summary:

Aggregation of the calculated add-ons across different hedging sets:

The asset class is interest rates; thus the applicable Supervisory factor is 0.50%. As a result:

 Add-on = SF × Effective Notional = 0.005 × 69,375,513 = 346,878

   Supervisory Correlation Parameters

Correlation is not applicable to the interest rate asset class, and there is no other asset class in the netting set in this example.

   Add-on Aggregation

For this netting set, the interest rate add-on is also the aggregate add-on because there are no trades assigned to other asset classes. Thus, the aggregate add-on = 346,878

   Multiplier

The multiplier is given by:

multiplier = min { 1; Floor+(1-Floor) × exp [(V-C) /(2 ×(1-Floor)×Add-on_agg)]}

   = min {1; 0.05 + 0.95 × exp [60,000 / (2 × 0.95 × 346,878]}

     =1

   Final Calculation of PFE

In this case the multiplier is equal to one, so the PFE is the same as the aggregate Add-On:

PFE = multiplier × Add-on_agg = 1 × 346,878 = 346,878
 

The exposure EAD to be risk weighted for counterparty credit risk capital requirements purposes is therefore

EAD = 1.4 * (RC + PFE) = 1.4 x (60,000 + 346,878) = 569,629
 

The replacement cost is calculated at the netting set level as a simple algebraic sum (floored at zero) of the derivatives’ market values at the reference date. Thus, using the market values indicated in the table (expressed in thousands):

RC = max {V - C; 0} = max {20 - 40 + 0; 0} = 0
 

Since V-C is negative (i.e. -20,000), the multiplier will be activated (i.e. it will be less than 1). Before calculating its value, the aggregate add-on needs to be determined.

The following table illustrates the steps typically followed for the add-on calculation:

   Effective Notional Amount

The adjusted notional of each trade is calculated by multiplying the notional amount with the calculated supervisory duration SD specified in the Standards.

d= Trade Notional × SD = Trade Notional × {exp(-0.05×S) – exp(-0.05 × E)} / 0.05

The appropriate supervisory delta must be assigned to each trade: in particular, since Trade 1 and Trade 3 are long in the primary risk factor (CDS spread), their delta is 1; in contrast, the supervisory delta for Trade 2 is -1.

Thus, the entity-level effective notional is equal to the adjusted notional times the supervisory delta times the maturity factor (where the maturity factor is 1 for all three derivatives).

   Supervisory Factor

The add-on must now be calculated for each entity. Note that all derivatives refer to different entities (single names/indices). A supervisory factor is assigned to each single-name entity based on the rating of the reference entity, as specified in Table 1 in the relevant Standards. This means assigning a supervisory factor of 0.38% for AA-rated firms (Trade 1) and 0.54% for BBB-rated firms (for Trade 2). For CDS indices (Trade 3), the supervisory factor is assigned according to whether the index is investment or speculative grade; in this example, its value is 0.38% since the index is investment grade.

Thus, the entity level add-ons are as follows:

Add-on(Entity) = SF × Effective Notional
 

Supervisory Correlation Parameters

The add-on calculation separates the entity level add-ons into systematic and idiosyncratic components, which are combined through weighting by the correlation factor. The correlation parameter ρ is equal to 0.5 for the single-name entities (Trade 1-Firm A and Trade 2-Firm B) and 0.8 for the index (Trade 3-CDX.IG) in accordance with the requirements of the Standards.

Add-on^(Credit) = [ [ ∑_k ρ_k ^CR × Add-on (Entity_k) ]² + ∑_k (1- (ρ_k ^CR)²) × (Add-on (Entity_k))²]^1/2

   Add-on Aggregation

For this netting set, the interest rate add-on is also the aggregate add-on because there are no trades assigned to other asset classes. Thus, the aggregate add-on = 346,878

Aggregation of entity-level add-ons with full offsetting in the systematic component and no offsetting benefit in the idiosyncratic component.

   Thus,

Add-on = [ (47,462)² + 77,344,042,776 ]^1/2 = 282,129

   Multiplier

   The multiplier is given by

multiplier = min {1; Floor+(1-Floor) × exp [(V-C)/(2×(1-Floor)×Add-on_agg)]}

   = min {1; 0.05 + 0.95 × exp [-20,000 / (2 × 0.95 × 282,129)]}

      =0.96521

   Final Calculation of PFE

PFE = multiplier × Add-on_agg = 0.96521 × 282,129= 272,313
 

The exposure that would be risk-weighted for the purpose of counterparty credit risk capital requirements is therefore:

EAD = 1.4 * (RC + PFE) = 1.4 x (0 + 272,313) = 381,238
 

The replacement cost is calculated at the netting set level as a simple algebraic sum (floored at zero) of the derivatives’ market values at the reference date, provided that value is positive. Thus, using the market values indicated in the table (expressed in thousands):

RC = max {V - C; 0} = max {100 - 30 - 50; 0} = 20
 

The replacement cost is positive and there is no exchange of collateral (so the bank has not received excess collateral), which means the multiplier will be equal to 1.

The following table illustrates the steps typically followed for the add-on calculation, for each of the four commodity hedging sets with non-zero exposure:

   Effective Notional Amount

Trade-level Adjusted Notional calculation for each commodity derivative trade:

d_i^(COM) = current price per unit × number of units in the trade
 

The appropriate supervisory delta must be assigned to each trade:

Since the remaining maturity of Trade 1 is less than a year, at nine months (approximately 187 business days), and the trade is un-margined, its maturity factor is scaled down by the square root of 187/250 in accordance with the requirements of the Standards. On the other hand, the maturity factor is 1 for Trade 2 and for Trade 3, since the remaining maturity of those two trades is greater than one year and they are un-margined.

The trade-level effective notional is equal to the adjusted notional times the supervisory delta times the maturity factor. The basic difference between the WTI and Brent forward contracts effectively is ignored since they belong to the same commodity type, namely “Crude Oil” within the “Energy” hedging set, thus allowing for full offsetting. (In contrast, if one of the two forward contracts were on a different commodity type within the “Energy” hedging set, such as natural gas, with the other on crude oil, then only partial offsetting would have been allowed between the two trades.) Therefore, Trade 1 and Trade 2 can be aggregated into a single effective notional, taking into account each trade’s supervisory delta and maturity factor.

   Supervisory Factor

For each commodity-type in a hedging set, the effective notional amount must be multiplied by the correct Supervisory Factor (SF). As described in the Standards, the Supervisory Factor for both the Crude Oil commodity type in the Energy hedging set and the Silver commodity type in the Metals hedging set is SF=18%.

Thus, the add-on by hedging set and commodity type is as follows:

Add-on(Type_k^j) = SF_Typek^(Com) × Effective Notional_Typek^(Com)
 

   Supervisory Correlation Parameters

The commodity-type add-ons in a hedging set are decomposed into systematic and idiosyncratic components. The commodity subclass correlations parameters are as stated in the Standards, in this case 40% for commodities.

Thus, the hedging set level add-ons are calculated for each commodity hedging set:

Add-on^(COM) = [( Σ_k ρ_j^(COM) × Add-on (Type_k^j) )² + Σ_k (1- (ρ_j^(COM) )²) × (Add-on (Type ^j))²]_k^1/2

However, in this example, since only one commodity type within the “Energy” hedging set is populated (i.e. all other commodity types within that hedging set have a zero add-on), the resulting add-on for the hedging set is the same as the add-on for the commodity type. This calculation shows that when there is only one commodity type within a commodity hedging set, the hedging-set add-on is equal to the absolute value of the commodity-type add-on. (The same comment applies to the commodity type “Silver” in the “Metals” hedging set.)

   Add-on Aggregation

Aggregation of commodity-type add-ons uses full offsetting in the systematic component and no offsetting benefit in the idiosyncratic component in each hedging set. As noted earlier, in this example there is only one commodity type per hedging set, which means no offsetting benefits. Computing the simple summation of absolute values of add-ons for the hedging sets:

Add-on = Σ_j Add-on_j

Add-On = 2,043 + 1,800 = 3,843

   Multiplier

The multiplier is given by

multiplier = min {1; Floor+(1-Floor) × exp [(V-C)/(2×(1-Floor)×Add-on_agg)]}

   = min {1; 0.05 + 0.95 × exp [20 / (2 × 0.95 × 3,843)]}

      = 1, since V-C is positive.

   Final Calculation of PFE

PFE = multiplier × Add-on_agg = 1 × 3,843 = 3,843
 

The exposure EAD to be risk weighted for counterparty credit risk capital requirements purposes is therefore

EAD = 1.4 * (RC + PFE) = 1.4 x (20 + 3,843) = 5,408